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Lecture
Presentation
Chapter 22
Current and
Resistance
© 2015 Pearson Education, Inc.
Suggested Videos for Chapter 22
• Prelecture Videos
• Current and Resistance:
Part 1
• Current and Resistance:
Part 2
• Current and Resistance:
Part 3
• Class Videos
• Determining Resistance
• Basic Circuits
• Practical Electrical
Applications
© 2015 Pearson Education, Inc.
• Video Tutor Solutions
• Current and Resistance
• Video Tutor Demos
• Resistance in Copper and
Nichrome
Slide 22-2
Suggested Simulations for Chapter 22
• PhETs
•
•
•
•
Battery Voltage
Signal Circuit
Resistance in a Wire
Circuit Construction Kit
(DC)
• Battery-Resistor Circuit
• Ohm’s Law
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Slide 22-3
Section 22.1 A Model of Current
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A Model of a Current
• If we connect the two capacitor plates of a parallel-plate
capacitor with a metal wire, the plates become neutral. The
capacitor has been discharged.
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Slide 22-22
A Model of a Current
• The motion of charges through a material is called a
current.
• If we observe a capacitor discharge, we see other effects.
As the capacitor discharges, the connecting wire gets
warmer.
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Slide 22-23
A Model of a Current
• As the capacitor discharges, if the wire is very thin in
places like the filament of a lightbulb, the wire gets hot
enough to glow.
• More current means a brighter bulb.
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Slide 22-24
A Model of a Current
• As the capacitor discharges, the current-carrying wire
deflects a compass needle.
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Slide 22-25
Charge Carriers
• The charges that move in a
current are called charge
carriers.
• In a metal, the charge
carriers are electrons.
• It is the motion of the
conduction electrons, which
are free to move around, that
forms a current in the metal.
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Slide 22-26
Charge Carriers
• An insulator does not have free charges and cannot carry a
current.
• Other materials may have different charge carriers. Both
positive and negative ions carry charge in ionic solutions
such as seawater, blood, and intercellular fluids.
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Slide 22-27
Creating a Current
• When we apply an electric field to a metal, the field exerts
a force on the electrons and they begin to accelerate.
• Collisions between the electrons and the atoms of the
metal slow them down, transforming the electron’s kinetic
energy into thermal energy, making the metal warmer.
• The motion of the electrons will cease unless you continue
pushing by maintaining an electric field.
• In a constant field, an electron’s average motion will be
opposite the field. The motion is the electron’s drift
velocity.
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Slide 22-28
Creating a Current
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Slide 22-29
Creating a Current
• In a parallel-plate capacitor, the initial separation of
charges creates a potential difference between the plates.
• Connecting a wire between the plates establishes an
electric field in the wire, which causes electrons to flow
from the negative plate (which has an excess of electrons)
toward the positive plate.
• The potential difference creates the electric field that
drives the current in the wire.
• Eventually the plates will be completely discharged,
meaning no more potential difference, no more field, and
no more current.
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Slide 22-30
Creating a Current
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Slide 22-31
Creating a Current
• The current at point B is exactly equal to the current at
point A.
• The current leaving a lightbulb is exactly the same as
the current entering the lightbulb.
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Slide 22-32
Creating a Current
• The lightbulb cannot destroy electrons without violating
the law of conservation of mass and the law of
conservation of charge. Thus, the number of electrons is
not changed by the lightbulb.
• The lightbulb cannot store electrons, or it would become
increasingly negative until its repulsive force would stop
the flow of new electrons and the bulb would go out.
• Every electron entering the lightbulb is matched by an
electron leaving the lightbulb, and thus the currents on
either side of a lightbulb are equal.
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Slide 22-33
Creating a Current
• Like with an electric
current and a lightbulb,
water flows through a
turbine, making it turn.
• The amount of water
leaving the turbine equals
the amount of water
entering the turbine.
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Slide 22-34
Creating a Current
• The water, like an electric
current, is doing work, so
there is an energy change.
• In a lightbulb, the energy is
dissipated by atomic-level
friction as the electrons
move through the wire,
making the wire hotter until
it glows.
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Slide 22-35
Creating a Current
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Slide 22-36
QuickCheck 22.1
A wire carries a current. If both the wire diameter and the
electron drift speed are doubled, the electron current
increases by a factor of
A.
B.
C.
D.
E.
2
4
6
8
Some other value
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Slide 22-37
QuickCheck 22.1
A wire carries a current. If both the wire diameter and the
electron drift speed are doubled, the electron current
increases by a factor of
A.
B.
C.
D.
E.
2
4
6
8
ie  Ad
Some other value
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Slide 22-38
Conceptual Example 22.1 Which bulb is
brighter?
The discharge of a capacitor lights
two identical bulbs, as shown in
FIGURE 22.8. Compare the
brightness of the two bulbs.
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Slide 22-39
Conceptual Example 22.1 Which bulb is
brighter? (cont.)
REASON Current
is conserved, so
any current that goes through
bulb 1 must go through bulb 2 as
well—the currents in the two
bulbs are equal.
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Slide 22-40
Conceptual Example 22.1 Which bulb is
brighter? (cont.)
We’ve noted that the brightness of
a bulb is proportional to the current
it carries. Identical bulbs carrying
equal currents must have the same
brightness.
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Slide 22-41
Conceptual Example 22.1 Which bulb is
brighter? (cont.)
ASSESS This
result makes sense in
terms of what we’ve seen about the
conservation of current. No charge
is “used up” by either bulb.
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Slide 22-42
Section 22.2 Defining and Describing Current
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Defining and Describing Current
• A capacitor discharges in the same way whether we
consider negative charges moving opposite the field, or
positive charges moving in the same direction as the field.
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Slide 22-44
Defining and Describing Current
• We adopt the
convention that the
current is the flow of
positive charge.
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Slide 22-45
Definition of Current
• Currents are charges in motion, so we define current as the
rate, in coulombs per second, at which charge moves
through a wire.
[Insert Figure 22.10]
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Slide 22-46
Definition of Current
• We measure the amount of charge Δq that passes through a
cross section of the wire in time interval Δt:
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Slide 22-47
Definition of Current
• The current direction in a wire is from higher potential to
lower potential, or in the direction of the electric field.
• Current is measured in coulombs/second, which we define
as an ampere A.
• 1 ampere = 1 A = 1 coulomb/second = 1 C/s
• Household currents are typically ~ 1 A or 1 amp
• For a steady current, the total amount of charge delivered
by a current I during time interval Δt is
q = I ∆t
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Slide 22-48
QuickCheck 22.2
Every minute, 120 C of charge flow through this cross
section of the wire.
The wire’s current is
A.
B.
C.
D.
E.
240 A
120 A
60 A
2A
Some other value
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Slide 22-49
QuickCheck 22.2
Every minute, 120 C of charge flow through this cross
section of the wire.
The wire’s current is
A.
B.
C.
D.
E.
240 A
120 A
60 A
2A
Some other value
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Slide 22-50
Example 22.2 Charge flow in a lightbulb
A 100 W lightbulb carries a current of 0.83 A. How much
charge flows through the bulb in 1 minute?
SOLVE According
to Equation 22.2, the total charge passing
through the bulb in 1 min = 60 s is
q = I ∆t = (0.83 A)(60 s) = 50 C
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Slide 22-51
Example 22.2 Charge flow in a lightbulb (cont.)
ASSESS The
current corresponds to a flow of a bit less than
1 C per second, so our calculation seems reasonable, but the
result is still somewhat surprising. That’s a lot of charge!
The enormous charge that flows through the bulb is a good
check on the concept of conservation of current. If even a
minuscule fraction of the charge stayed in the bulb, the bulb
would become highly charged.
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Slide 22-52
Example 22.2 Charge flow in a lightbulb (cont.)
For comparison, a Van de Graaff generator develops a
potential of several hundred thousand volts due to an excess
charge of just a few C, a ten-millionth of the charge that
flows through the bulb in 1 minute. Lightbulbs do not
develop a noticeable charge, so the current into and out of
the bulb must be exactly the same.
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Slide 22-53
Example Problem
The discharge of the electric eel can transfer a charge of
2.0 mC in a time of 2.0 ms. What current, in A, does this
correspond to?
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Slide 22-54
QuickCheck 22.3
A and B are identical lightbulbs connected to a battery as
shown. Which is brighter?
A. Bulb A
B. Bulb B
C. The bulbs are equally bright.
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Slide 22-55
QuickCheck 22.3
A and B are identical lightbulbs connected to a battery as
shown. Which is brighter?
A. Bulb A
B. Bulb B
C. The bulbs are equally bright.
Conservation of current
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Slide 22-56
Conservation of Current at a Junction
• A junction is a point where a
wire branches.
• For a junction, the law of
conservation requires
ΣIin = ΣIout
• The basic conservation
statement, that the sum of the
currents into a junction equals
the sum of the currents
leaving, is called Kirchhoff’s
junction law.
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Slide 22-57
QuickCheck 22.4
The wires shown next carry currents as noted. Rate the
currents IA, IB, and IC.
A.
B.
C.
D.
E.
IA > IB > IC
IB > IA > IC
IC > IA > IB
IA > IC > IB
IC > IB > IA
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Slide 22-58
QuickCheck 22.4
The wires shown next carry currents as noted. Rate the
currents IA, IB, and IC.
A.
B.
C.
D.
E.
IA > IB > IC
IB > IA > IC
IC > IA > IB
IA > IC > IB
IC > IB > IA
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Slide 22-59
QuickCheck 22.5
The current in the fourth wire is
A.
B.
C.
D.
E.
16 A to the right.
4 A to the left.
2 A to the right.
2 A to the left.
Not enough information to tell
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Slide 22-60
QuickCheck 22.5
The current in the fourth wire is
A.
B.
C.
D.
E.
16 A to the right.
4 A to the left.
2 A to the right.
2 A to the left. Conservation of current
Not enough information to tell
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Slide 22-61
Example 22.3 Currents in a junction
Four wires have currents as noted
in FIGURE 22.12. What are the
direction and the magnitude of the
current in the fifth wire?
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Slide 22-62
Example 22.3 Currents in a junction (cont.)
PREPARE This
is a conservation of
current problem. We compute the
sum of the currents coming into
the junction and the sum of the
currents going out of the junction,
and then compare these two sums.
The unknown current is whatever
is required to make the currents
into and out of the junction “balance.”
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Slide 22-63
Example 22.3 Currents in a junction (cont.)
SOLVE Two
of the wires have
currents into the junction:
ΣIin = 3 A + 4 A = 7 A
Two of the wires have currents out
of the junction:
ΣIout = 6 A + 2 A = 8 A
To conserve current, the fifth wire
must carry a current of 1 A into the
junction.
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Slide 22-64
Example 22.3 Currents in a junction (cont.)
If the unknown current is
1 A into the junction, a total of
8 A flows in—exactly what is
needed to balance the current
going out.
ASSESS
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Slide 22-65